Process parameter and state estimation

Eykhoff, P.

doi:10.1016/0005-1098(68)90015-0

Cited by 96 publications

(101 citation statements)

References 5 publications

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“…The IV algorithm is by no means the only estimator suitable for the classical input/output models of time-series analysis ; there are several others [e.g., Astrom and Bohlin, 1966;Box and Jenkins, 1970;Astrom and Eykhoff, 1971 ;Eykhoff, 1974], most of which can be written in recursive form [Soderstrom et al, 1978]. Gentil [1984], for instance, has reported an interesting example for the analysis of phytoplankton-zooplankton dynamics in Lake Aiguebelette, France, using a recursive version of a maximum likelihood estimator.…”

Section: Time (Days)mentioning

confidence: 99%

“…The texts by Eykhoff [1974], Young [1984], and to a lesser extent, Jazwinski [1970], Schweppe [1973], andGelb [1974] provide very good introductions to the subject; the recent books by Ljung and Soderstrom [1983] and Soderstrom and Stoica [1983] give a more advanced treatment of the theoretical underpinnings of the subject, especially with respect to recursive estimation algorithms and the input/output class III model structures; and there have also been some important review and tutorial papers, of which those by Astrom and Eykhoff [1971], Isermann [1981], and Young [1981] are most relevant to the present discussion. This is, of course, a biased sample of the literature, for it reflects solely the control theoretic view of the subject and, with the possible exception of Young [1984], makes little reference to the undoubtedly substantial contributions from statistics and econometrics.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…But since the former have already been discussed in section 4 and since they do not reflect the vast majority of applications to the problem of parameter estimation, it is convenient to concentrate here on batch estimation algorithms. The four estimators are distinguished in an ascending order of the degree of completeness in accounting for the various sources of uncertainty (as in the work by Eykhoff [1974] Here the summation is over the N sets of errors e(tk) for all the sampled observation instants tk. Equation (22) emphasizes the fact that e is a function of estimates of both the states and parameters, although in most instances the determination of the minimum value of J will be achieved by adjusting only the values of the (constant) parameters ( cc) and not the values of the states for all the instants tk, i.e., ( x(tk) ) .…”

Section: Types Of Estimatormentioning

confidence: 99%

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Water quality modeling: A review of the analysis of uncertainty

Beck¹

1987

Water Resources Research

870

431

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This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first‐order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.

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Section: Time (Days)mentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: Types Of Estimatormentioning

confidence: 99%

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Water quality modeling: A review of the analysis of uncertainty

Beck¹

1987

Water Resources Research

870

431

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“…A lower bound for the parameter variance-covariance is provided by the CramerRao inequality (see, for example, Eykhoff, 1974): (14) where J is the Fisher information matrix:…”

Section: Parameter Variance-covariancementioning

confidence: 99%

“…This topic is usually associated with control theory, statistics, and econometrics, and may perhaps be considered an intruder in water quality modeling (Astrom and Eykhoff, 1971;Eykhoff, 1974). An impressive array of techniques has been developed for the analysis of relatively conventional, well-posed problems, such as those encountered in identifying models for aircraft dynamics, chemical unit processes, and physiological systems (see Isermann, 1980), but water quality model identification involves problems that are not at all well-posed so that these techniques may not· be applied in any straightforward way.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty and Forecasting of Water Quality

1983

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Non‐parametric identification of a class of non‐linear close‐coupled dynamic systems

Udwadia

Kuo

1981

Earthq Engng Struct Dyn

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A non‐parametric identification technique for the identification of arbitrary memoryless non‐linearities has been presented for a class of close‐coupled dynamic systems which are commonly met with in mechanical and structural engineering. The method is essentially a regression technique and expresses the non‐linearities as series expansions in terms of orthogonal functions. Whereas no limitation on the type of test signals is imposed, the method requires the monitoring of the response of each of the masses in the system. The computational efficiency of the method, its easy implementation on analogue and digital machines and its relative insensitivity to measurement noise make it an attractive approach to the non‐parametric identification problem.

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Process parameter and state estimation

Cited by 96 publications

References 5 publications

Water quality modeling: A review of the analysis of uncertainty

Water quality modeling: A review of the analysis of uncertainty

Uncertainty and Forecasting of Water Quality

Non‐parametric identification of a class of non‐linear close‐coupled dynamic systems

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